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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>The cube root of 125 is the value “y” such that the number “y” is multiplied 3 thrice by itself. ∛ is the symbol used to denote the cube root of a number. Cube roots are used in designing loudspeakers or in pharmacology for correct dosage of medicine as per body weight.</p>

4 <h2>What Is the Cube Root of 125?</h2>

5 <p>The<a>cube</a>root of 125 is 5. The cube root of 125 is expressed as ∛125 in radical form, where the “∛" sign is called the “radical” sign. In<a>exponential form</a>, it is written as (125)⅓ </p>

6 <h2>Finding the Cube Root of 125</h2>

7 <p>We can find the<a>cube root</a>of 125 through various methods. </p>

8 <ul><li>Prime Factorization method</li>

9 </ul><ul><li>Subtraction method </li>

10 </ul><h3>Cube Root of 125 By Prime Factorization</h3>

11 <p>Finding a cube root of 125 through the Prime Factorization method involves determining the<a>factor</a>of 125.</p>

12 <p><strong>Step 1:</strong>Find the<a>prime factors</a>of 125.</p>

13 <p>So, 125 = 5x5x5 </p>

14 <p><strong>Step 2:</strong>Group the factors of 125 in a group of 3.</p>

15 <p><strong>Step 3: </strong>Since 125 is a<a>perfect cube</a>, we have a pair of 3, so there is no need to expand it further.</p>

16 <p>The cube root of 125 can be written as ∛125 = ∛5x5x5 = 5 </p>

17 <p>Therefore, the cube root of 125 is 5. </p>

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20 <h3>Cube Root of 125 By Subtraction Method</h3>

19 <h3>Cube Root of 125 By Subtraction Method</h3>

21 <p>In this method, from the given cube<a>number</a>, 1, 7, 19, 37, 61, 91, 127, 169... are successively subtracted till we get zero. The number of times<a>subtraction</a>was performed gives the cube root of the given number. </p>

20 <p>In this method, from the given cube<a>number</a>, 1, 7, 19, 37, 61, 91, 127, 169... are successively subtracted till we get zero. The number of times<a>subtraction</a>was performed gives the cube root of the given number. </p>

22 <p><strong>Step 1:</strong>Subtract the 1st<a>odd number</a>: 125 - 1 = 124 </p>

21 <p><strong>Step 1:</strong>Subtract the 1st<a>odd number</a>: 125 - 1 = 124 </p>

23 <p><strong>Step 2:</strong>Subtract the next odd number: 124 - 7 = 117</p>

22 <p><strong>Step 2:</strong>Subtract the next odd number: 124 - 7 = 117</p>

24 <p><strong>Step 3:</strong>Subtract the next odd number: 117 - 19 = 98</p>

23 <p><strong>Step 3:</strong>Subtract the next odd number: 117 - 19 = 98</p>

25 <p><strong>Step 4:</strong>Subtract the next odd number: 98 - 37 = 61 </p>

24 <p><strong>Step 4:</strong>Subtract the next odd number: 98 - 37 = 61 </p>

26 <p><strong>Step 5:</strong>Subtract the next odd number: 61 - 61 = 0</p>

25 <p><strong>Step 5:</strong>Subtract the next odd number: 61 - 61 = 0</p>

27 <p>Here the subtraction took place five times to reach zero.</p>

26 <p>Here the subtraction took place five times to reach zero.</p>

28 <p>Hence the cube root of 125 is 5. </p>

27 <p>Hence the cube root of 125 is 5. </p>

29 <h2>Common Mistakes and How to Avoid Them in the Cube Root of 125</h2>

28 <h2>Common Mistakes and How to Avoid Them in the Cube Root of 125</h2>

30 <p>While finding the cube root of 125, there are some common mistakes that we often make. So let’s discuss a few of the mistakes and their solutions. </p>

29 <p>While finding the cube root of 125, there are some common mistakes that we often make. So let’s discuss a few of the mistakes and their solutions. </p>

30 + <h2>Download Worksheets</h2>

31 <h3>Problem 1</h3>

32 <p>A cube-shaped container has a volume of 125 cubic cm. What is the length of one side of the container?</p>

33 <p>Okay, lets begin</p>

34 <p>5 centimeters. </p>

35 <h3>Explanation</h3>

36 <p>The cube root of 125 is 5, so the length of one side is 5 cm.</p>

37 <p>Well explained 👍</p>

38 <h3>Problem 2</h3>

39 <p>Find the value of x in the equation: x³ = 125</p>

40 <p>Okay, lets begin</p>

41 <p>x = 5 </p>

42 <h3>Explanation</h3>

43 <p>the cube root of 125 is 5.</p>

44 <p>Well explained 👍</p>

45 <h3>Problem 3</h3>

46 <p>Simplify the expression: √(125)</p>

47 <p>Okay, lets begin</p>

48 <p> 5 * √5. </p>

49 <h3>Explanation</h3>

50 <p> √(125) can be written as √(5³) = 53/2 </p>

51 <p>Well explained 👍</p>

52 <h3>Problem 4</h3>

53 <p>A spherical ball has a volume of 125 cubic inches. What is the radius of the ball (to the nearest inch)?</p>

54 <p>Okay, lets begin</p>

55 <p>3 inches. </p>

56 <h3>Explanation</h3>

57 <p> The volume of a sphere is (4/3)πr³. Setting this equal to 125 and solving for r, we find that r = 3 inches. </p>

58 <p>Well explained 👍</p>

59 <h3>Problem 5</h3>

60 <p>A cube-shaped box has a surface area of 150 square units. What is the volume of the box?</p>

61 <p>Okay, lets begin</p>

62 <p>125 cubic units. </p>

63 <h3>Explanation</h3>

64 <p>First, find the side length of the cube. The surface area of a cube is 6s². Solving for s, we get s = 5.</p>

65 <p>Then, the volume is s³, which is 125 cubic units. </p>

66 <p>Well explained 👍</p>

67 <h3>Conclusion</h3>

68 <p>We get a cube root of a number when multiplied by itself three times. Methods like Prime Factorization, and subtraction methods are useful in finding the cube root of a perfect cube. Since we have found the cube root of 125 using all these methods, it has become quite simple to find the cube roots of any other number. </p>

69 <h2>FAQs on 125 Cube Root</h2>

70 <h3>1.Cube root of 125?</h3>

71 <h3>2.Is 125 a perfect cube?</h3>

72 <p>125 is a perfect cube because it can as 5x5x5</p>

73 <h3>3.What is the cube root of -125?</h3>

74 <p> Cube root of -125 will be -5. </p>

75 <h3>4.Is the cube root of 125 a rational number?</h3>

76 <h3>5.Is there any shortcut to find the cube of any number?</h3>

77 <p>There is no shortcut to find the cube root of any number. The best way to go is with the prescribed and standard methods. </p>

78 <h3>Important Glossaries for Cube Root of 125</h3>

79 <ul><li><strong>Perfect cube:</strong> Perfect cube is the number that can be expressed as the cube of an integer. </li>

80 </ul><p>As 125 = 5x5x5, it is a perfect cube </p>

81 <ul><li><strong>Radical form:</strong>It’s the notation used to represent roots, ∛125</li>

82 </ul><ul><li><strong>Exponent form:</strong>It’s the notation used to represent roots using exponents, (125)⅓</li>

83 </ul><ul><li><strong>Equation:</strong>It is a mathematical expression that asserts the quality of two expressions. </li>

84 </ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>

85 <p>▶</p>

86 <h2>Jaskaran Singh Saluja</h2>

87 <h3>About the Author</h3>

88 <p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>

89 <h3>Fun Fact</h3>

90 <p>: He loves to play the quiz with kids through algebra to make kids love it.</p>